Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)2291610.22363/2658-4670-2019-27-4-343-354Research ArticleVine copulas structures modeling on Russian stock marketShchetininEugeny Yu.<p>Doctor of Physical and Mathematical Sciences, lecturer of Department of Data Analysis, Decision Making and Financial Technologies</p>riviera-molto@mail.ruFinancial University under the Government of Russian Federation1512201927434335419022020Copyright © 2019, Shchetinin E.Y.2019<p>Pair-copula constructions have proven to be a useful tool in statistical modeling, particularly in the field of finance. The copula-based approach can be used to choose a model that describes the dependence structure and marginal behaviour of the data in efficient way, but is usually applied to pairs of securities. In contrast, vine copulas provide greater flexibility and permit the modeling of complex dependency patterns using the rich variety of bivariate copulas which may be arranged and analysed in a tree structure. However, the number of possible configurations of a vine copula grows exponentially as the number of variables increases, making model selection a major challenge in development. So, to learn the best possible model, one has to identify the best possible structure, which necessitates identifying the connections between the variables and selecting between the multiple bivariate copulas for each pair in the structure. This paper features the use of regular vine copulas in analysis of the co-dependencies of four major Russian Stock Market securities such as Gazprom, Sberbank, Rosneft and FGC UES, represented by the RTS index. For these stocks the D-vine structures of bivariate copulas were constructed, which models are described by Gumbel, Student, BB1and BB7 copulas, and estimates of their parameters were obtained. Computer simulations showed a high accuracy of the approximation of the explored data by D-vine structure of bivariate copulas and the effectiveness of our approach in general.</p>copulamultivariate modelsdependence structurevinessecuritiesфинансовый анализценные бумагимногомерные структуры статистических связейкопулывьющиеся копулы[K. Aas and I. Hobaek Haff, “The generalized hyperbolic skew Student’s t-distribution,” Journal of Financial Econometrics, vol. 4, pp. 275-309, Jan. 2006. DOI: 10.1093/jjfinec/nbj006.][K. Aas, C. Czado, A. Frigessi, and H. Bakken, “Pair-copula constructions of multiple dependence,” Insurance: Mathematics and Economics, vol. 44, no. 2, pp. 182-198, 2009.][D. Berg, “Copula goodness-of-fit testing: an overview and power comparison,” European Journal of Finance, vol. 15, pp. 675-701, 2009. DOI: 10.1080/13518470802697428.][T. Bedford and R. M. Cooke, “Vines-a new graphical model for dependent random variables,” The Annals of Statistics, vol. 30, no. 4, pp. 1031- 1068, 2002. DOI: 10.1214/aos/1031689016.][A. Panagiotelis, C. Czado, H. Joe, and J. Stöber, “Model selection for discrete regular vine copulas,” Comput. Stat. Data Anal., vol. 106, pp. 138-152, 2017. DOI: 10.1016/j.csda.2016.09.007.][J.-D. Fermanian, “Recent developments in copula models,” Econometrics, vol. 5, no. 34, 2017. DOI: 10.3390/econometrics5030034.][R. B. Nelsen, An introduction to copulas. New York: Springer, 1999.][H. Joe, H. Li, and A. K. Nikoloulopoulos, “Tail dependence functions and vine copulas,” Journal of Multivariate Analysis, vol. 101, pp. 252- 270, 2010. DOI: 10.1016/j.jmva.2009.08.002.][H. Joe, “Dependence comparisons of vine copulae with four or more variables,” in D. Kurowicka and H. Joe (Eds.), Dependence Modeling. Singapore: World Scientific, 2010.][A. K. Nikoloulopoulos, H. Joe, and H. Li, “Vine copulas with asymmetric tail dependence and applications to financial return data,” Computational Statistics and Data Analysis, vol. 56, no. 11, pp. 3659-3673, 2012.][Modeling dependence in econometrics. Berlin, Heidelberg: Springer Verlag, 2014. DOI: 10.1007/978-3-319-03395-2.][A. J. Patton, “Modelling asymetric exchange rate dependence,” International Economic Review, vol. 47, no. 2, pp. 527-556, 2006. DOI: 10.1111/j.1468-2354.2006.00387.x.][E. C. Brechmann, C. Czado, and K. Aas, “Truncated regular vines in high dimensions with application to financial data,” Canadian Journal of Statistics, vol. 40, no. 1, pp. 68-85, 2012. DOI: 10.1002/cjs.10141.][J. Di’́smann, E. Brechmann, C. Czado, and D. Kurowicka, “Selecting and estimating regular vine copulae and application to financial returns,” Computational Statistics & Data Analysis, vol. 59, pp. 52-69, 2013. DOI: 10.1016/j.csda.2012.09.01.][E. C. Brechmann and U. Schepsmeier, “Modeling dependence with Cand D-vine copulas: the R package CDVine,” Journal of Statistical Software, vol. 52, no. 3, pp. 1-27, 2013. DOI: 10.18637/jss.v052.i03.][S. Konishi and G. Kitagawa, Information criteria and statistical modeling. 2007. DOI: 10.1007/978-0-387-71887-3.][H. Manner and O. Reznikova, “A survey on time-varying copulas: specification, simulations and application,” Econometric Reviews, vol. 31, no. 6, pp. 654-687, 2012. DOI: 10.1080/07474938.2011.608042.][L. Chollete, A. Heinen, and A. Valdesogo, “Modeling international financial returns with a multivariate regime switching copula,” J. Financ. Econ., vol. 7, pp. 437-480, 2009. DOI: 10.2139/ssrn.1102632.][T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to algorithms, 2rd Edition. MIT Press, 2001.][D. E. Allen, M. A. Ashraf, M. McAleer, R. J. Powell, and A. K. Singh, “Financial dependence analysis: applications of vine copulas,” Statistica Neerlandica, vol. 67, no. 4, pp. 403-435, 2013. DOI: 10. 1111 / stan. 12015.]